U.S. patent number 7,420,366 [Application Number 10/874,009] was granted by the patent office on 2008-09-02 for coupled nonlinear sensor system.
This patent grant is currently assigned to The United States of America as represented by the Secretary of the Navy. Invention is credited to Adi R. Bulsara, Visarath In, Yong Kho, Antonio Palacios.
United States Patent |
7,420,366 |
In , et al. |
September 2, 2008 |
Coupled nonlinear sensor system
Abstract
A sensor system employing a plurality of nonlinear sensors
utilizes a coupling network to interconnect the sensors wherein the
coupling network inherently induces oscillations in the sensor
system. This approach removes the need to provide bias signal
generation either onboard the sensors or via a source external to
the sensor.
Inventors: |
In; Visarath (Chula Vista,
CA), Palacios; Antonio (San Diego, CA), Kho; Yong
(San Diego, CA), Bulsara; Adi R. (San Diego, CA) |
Assignee: |
The United States of America as
represented by the Secretary of the Navy (Washington,
DC)
|
Family
ID: |
39718394 |
Appl.
No.: |
10/874,009 |
Filed: |
June 18, 2004 |
Current U.S.
Class: |
324/253;
324/244 |
Current CPC
Class: |
G01R
33/04 (20130101) |
Current International
Class: |
G01R
33/04 (20060101) |
Field of
Search: |
;324/247,253,109,244,248,254,255,301,519,686
;73/1.15,1.48,1.49,1.51,35.11,35.13,514.34,514.32,721,727 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Visarath et al., Experimental Observation of Multifrequency
Patterns in Arrays of Coupled Nonlinear Oscillators, Physical
Review Letters, vol. 91, No. 24, published Dec. 11, 2003, 4 pages.
cited by examiner .
Visarath In, et al., Coupling-induced oscillations in overdamped
bistable systems, The American Physical Society, Physical Review E
68, 045102(R) (2003) pp. 045102-1 to 045102-4. cited by other .
Adi R. Bulsara et al., Emergent Oscillations in Unidirectionally
Coupled Overdamped Bistable Systems, dated: Feb. 12, 2004. p. 1-12.
cited by other.
|
Primary Examiner: Assouad; Patrick
Assistant Examiner: Schindler; David M.
Attorney, Agent or Firm: Eppele; Kyle Lipovsky; Peter A.
Anderson; J. Eric
Claims
What is claimed is:
1. An apparatus comprising: an odd number of at least three
nonlinear sensors each having an input and an output; and a
coupling network configured to inherently induce oscillation in
said nonlinear sensors in the absence of an external bias signal,
said coupling network including a coupling circuit individual to
each of said nonlinear sensors, said coupling network
unidirectionally coupling said nonlinear sensors so that each said
nonlinear sensor has its said output coupled via its coupling
circuit to said input of only one other said nonlinear sensor
wherein said coupling circuits are configured to allow only one-way
signal flow between said sensors that are nearest-neighbor
sensors.
2. The apparatus of claim 1 further including a summer connected to
each said coupling circuit individual to each of said nonlinear
sensors to sum a coupling circuit output from each of said
nonlinear sensors.
3. The apparatus of claim 2 wherein each of said nonlinear sensors
is one-dimensional.
4. The apparatus of claim 1 wherein each of said nonlinear sensors
is a magnetic fluxgate.
5. The apparatus of claim 4 wherein said one-way signal flow
between said sensors follows a circuitous path in said coupling
network.
6. The apparatus of claim 1 wherein said nonlinear sensors are
chosen from the group of magnetic sensors, ferro-electric sensors,
and piezo-electric sensors.
7. An apparatus comprising: an odd number of at least three
nonlinear sensors each having an input and an output; a coupling
network configured to inherently induce oscillation in said
nonlinear sensors in the absence of an external bias signal, said
coupling network including a coupling circuit individual to each of
said nonlinear sensors, said coupling network unidirectionally
coupling said nonlinear sensors so that each said nonlinear sensor
has its said output coupled via its said coupling circuit to said
input of only one other said nonlinear sensor, said coupling
network providing one-way signal flow between said sensors that are
nearest-neighbor sensors; and a summer connected to each said
coupling circuit individual to each of said nonlinear sensors to
sum a coupling circuit output from each of said nonlinear
sensors.
8. The apparatus of claim 7 wherein each of said nonlinear sensors
is a magnetic fluxgate.
9. The apparatus of claim 7 wherein said one-way signal flow
between said sensors follows a circuitous path in said coupling
network.
10. The apparatus of claim 7 wherein said nonlinear sensors are
chosen from the group of magnetic sensors, ferro-electric sensors,
and piezo-electric sensors.
11. An apparatus comprising: three magnetic fluxgate sensors each
having an input and an output; a coupling network configured to
inherently induce oscillation in said magnetic fluxgate sensors in
the absence of an external bias signal, said coupling network
including a coupling circuit individual to each of said magnetic
fluxgate sensors, said coupling network unidirectionally coupling
said magnetic fluxgate sensors so that each said magnetic fluxgate
sensor has its said output coupled via its said coupling circuit
individual to each of said magnetic fluxgate sensors to said input
of only one other said magnetic fluxgate sensor, said coupling
network providing one-way signal flow between said magnetic
fluxgate sensors that are nearest-neighbor magnetic fluxgate
sensors, wherein said one-way signal flow between said magnetic
fluxgate sensors follows a circuitous path in said coupling
network; and a summer connected to each of said coupling circuits
individual to each of said magnetic fluxgate sensors to sum a
coupling circuit output from each of said magnetic fluxgate
sensors.
Description
BACKGROUND
Certain sensor systems involve nonlinear sensors that utilize a
known time-periodic bias signal to excite the sensors to oscillate.
A target signal is detected by noting its effect on the sensor's
oscillation level-crossing statistics. These sensing techniques are
accurately represented via the dynamics of overdamped bistable
systems; as such, their solutions (in the absence of any driving
signals or noise) are those that decay rapidly to one of the stable
steady states of the detector system. Yet, for nonlinear sensors to
effectively serve as detectors of target signals, the sensors need
to be operated as a device that switches between its stable
attractors, thereby enabling one to quantify the target signal via
its effect on the sensor switching dynamics. A bias signal that
promotes this switching can be provided by a signal generator
onboard the sensor system, however this can increase the power
budget of the sensor as well as contribute to the sensor's noise
floor.
SUMMARY
A sensor system employing a plurality of nonlinear sensors utilizes
a coupling network that interconnects the sensors to induce
inherent oscillations in the sensor system. This approach replaces
the need for bias signal generation either onboard the sensor
system or via a source external to the sensor system.
Other objects, advantages and new features of the invention will
become apparent from the following detailed description of the
invention when considered in conjunction with the accompanied
drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a symbolic representation of an example sensor
system.
FIG. 2 shows a time series plot of sensor waveforms.
FIG. 3A depicts a representative sensor system in block diagram
format whereas FIGS. 3B1-3B3 illustrate a more detailed
presentation of such a system.
FIG. 4 shows time series data collected from a representative
sensor system.
FIGS. 5A and B depict residence time data.
FIGS. 6A-6E are symbolic representations of additional example
sensor systems.
DESCRIPTION
A coupling network inherently induces oscillation in coupled
non-linear sensors in the absence of an external bias signal or a
signal generator signal provided onboard the employed sensors. As
an example, by coupling a given number of nonlinear sensors using
cyclic boundary conditions and uni-directional (one-way signal
flow) coupling, one can generate oscillatory solutions past a
critical value of coupling coefficient. Referring now to FIG. 1,
consider a sensor system 10 employing the dynamics of an
odd-number, for example three, of uni-directionally coupled,
nearest-neighbor fluxgate magnetometers 12, each of which are shown
employed with uni-directional couplings 14 that in conjunction with
each other make up a coupling network. The three nearest neighbor
magnetometers in this example are shown with "nearest-neighbor"
coupling. "Nearest-neighbor" and "nearest neighbor coupling" have
their usual meaning in the art herein, wherein an example
nearest-neighbor-coupling has a sensor x.sub.i coupled to sensors
x.sub.i+1, and x.sub.i-1. Use of periodic boundary conditions
compels the final sensor to be coupled to the first. Fluxgate
magnetometer devices are considered sensitive and inexpensive
detectors of magnetic signals and can be described as follows: {dot
over (x)}.sub.1=-x.sub.1+tan h(c(x.sub.1+.lamda.x.sub.2+.epsilon.))
{dot over (x)}.sub.2=-x.sub.2+tan
h(c(x.sub.2+.lamda.x.sub.3+.epsilon.)) {dot over
(x)}.sub.3=-x.sub.3+tan h(c(x.sub.3+.lamda.x.sub.1+.epsilon.))
(1)
Notice that the (unidirectional) coupling term, having strength
.lamda., (which in this example is assumed to be equal for all
three elements) is inside the nonlinearity term, a direct result of
the mean-field nature of the description (in the fluxgate
magnetometer, the coupling is effectuated through the induction in
the driving/excitation "pick up" coil of the magnetometer). In the
equations above, x.sub.i(t) represents the magnetic flux in the
i.sub.th magnetometer using suitably normalized units, and c is a
(temperature-dependent) parameter for each magnetometer element.
The individual dynamics of each element are bistable for c>1.
For the equations above, state variables x.sub.1, x.sub.2, and
x.sub.3 provide a way to introduce the initial conditions of the
magnetometers. Finally, .epsilon. is a weak target signal that is
provided as a magnetometer input. Typically, it is this signal that
is desired to be detected.
A simple numerical integration of (1) (starting with non-identical
initial conditions) reveals oscillatory behavior for
.lamda.<.lamda..sub.c where .lamda..sub.c is a critical
threshold value of coupling strength. It will become apparent later
that .lamda..sub.c<0 in the convention adopted in (1). The
oscillations are non-sinusoidal, with a frequency that increases as
the coupling strength decreases away from .lamda..sub.c. For
.lamda.>.lamda..sub.c, however, the system quickly settles into
a steady state that depends on the initial conditions. In
experimentation, randomization of the initial conditions was found
to easily occur due to inherent noise in the sensor system. Even a
slight variation in the initial conditions, away from
x.sub.1=x.sub.2=x.sub.3, will push the system into the oscillatory
solution. For practical purposes, operational constraints (e.g. a
noise-floor) will compel non-equal initial conditions.
For the system described by Eq. (1), we may use the underlying
nonlinear dynamics to obtain the critical coupling strength
parameter .lamda..sub.c (for the onset of oscillations) as well as
the oscillation frequency .omega., in terms of the system and
target signal parameters:
.lamda..times..function..function..function..omega..apprxeq..function..fu-
nction..function..lamda..lamda..lamda..lamda..times.
##EQU00001##
The summed oscillations are not sinusoidal. However, they tend to
be sinusoidal for large coupling strength magnitude
(.lamda.<<.lamda..sub.c; recall that .lamda..sub.c<0). It
is instructive to note that there is a precise 2.pi./3 phase
difference between solutions, see FIG. 2 (for N coupled nonlinear
sensors, this phase offset will be 2.pi./N. Further, the summed
output of the sensor system is almost perfectly sinusoidal, having
frequency 3.omega. (N.omega. in general). In FIG. 2, there is shown
a time series plot of individual waveforms x.sub.1(t), x.sub.2(t)
and x.sub.3(t) (in light lines) and their sum (dark line) for c=3,
.lamda.=0.650 and .epsilon.=0.
Numerical simulations and calculations with (3) show that .omega.
is very sensitive to small changes in the target signal strength
.epsilon.; in addition, the mean value of the oscillation amplitude
is non-zero for finite .epsilon.. Both of these effects can be used
to quantify a very weak "target" signal .epsilon.. A very small
power source should suffice to sustain the oscillations once the
sensor system initially oscillates.
The summed response X(t) of the sensors has been observed to be
particularly sensitive to the presence of a target signal.
Numerical simulations show that the mean amplitude of X(t) can be
an order of magnitude or more in excess of the corresponding
response of a single uncoupled sensor that is externally driven to
generate oscillations similar to those shown in FIG. 2. Hence, the
inherent oscillation scheme described herein affords the
possibility of low sensor system power requirements and high
sensitivity.
In the presence of a noise-floor in each nonlinear sensor, one
would expect not to observe a significant change (introduced solely
by the noise) in the frequency .omega., as long as the noise
strength is much smaller than the energy barrier height in the
absence of coupling, noting that the generated oscillations are
suprathreshold. The noise-floor also provides needed non-identical
initial conditions in the elements of the array.
The target signal may be quantified, for example, via the change in
oscillation frequency of the sensor system as well as through a
computation of the mean values <x.sub.i(t)> or <X(t)>,
or even through spectral or level-crossing techniques.
FIG. 3A shows a block diagram format sensor setup using three
Printed-Circuit-Board (PCB)--technology based fluxgate
magnetometers, for example. The output of the fluxgates may be
taken directly as the magnetic flux response, or a voltage obtained
by differentiating the flux response with respect to time (see FIG.
4). Experiments show that the flux response is more sensitive,
which is in excellent agreement with the numerical simulation
results. In addition, it has been observed that by carefully tuning
the coupling strength so that the system is poised just beyond the
oscillation threshold (i.e. the oscillation frequency is low),
significantly greater sensitivity can be achieved, see FIGS. 5A-5B.
Further description will be provided herein as to an example way in
which this coupling strength can be adjusted.
FIG. 5A shows a plot of the residence time difference (left axis)
between upper and lower oscillating states versus coupling
strength. It also shows a plot of the residence time ratio between
the upper and lower oscillating states versus coupling strength.
Either method can be used to detect the target signal. The slope of
the curve represents the sensitivity of the device to detect a
target signal. This plot is produced with the target signal
strength at .epsilon.=0.1, and .lamda. varies from -1.0 to -0.54
which is near the bifurcation point (onset of oscillation) for the
particular value of .epsilon.=0.1. Sensitivity in this case is
taken to be proportional to the mean difference in residence times
in the stable states of a 2-threshold system, to which the summed
output is applied. FIG. 5B shows the marked enhanced sensitivity
achievable by coupled sensors (upper graph) versus that of a single
sensor (lower graph). The slope of the curve is defined as the
sensitivity of the response, wherein a constant slope reflects a
constant sensitivity. Near the onset of bifurcation, the slope
rises nearly vertically indicating a great sensitivity in that
region.
Turning now to further details of FIG. 3A, an example sensor system
16 involves three coupled fluxgate magnetometers 18.sub.n wherein n
in this example is three. Magnetometers 18.sub.n each have an
output 20.sub.n and input 22.sub.n. As can be seen, output 20.sub.1
of magnetometer 18.sub.1 is coupled to provide a corresponding
input to magnetometer 18.sub.2 by way of coupling elements
24.sub.1, 26.sub.1, 28.sub.1, 30.sub.1 and 32.sub.1 collectively
making up a coupling circuit 34.sub.1 and similarly for each of the
magnetometers wherein the combined coupling elements and their
interconnections with the magnetometers make up a coupling network
that as described herein generates an inherent oscillation in
system 16. Example PCB technology based fluxgates are made of
Cobalt-based trademark Metglas 2714A material as their cores and
each is sandwiched between two sheets of PCB material. The sides of
the PCB sheets that face away from the core material are printed
with copper wirings to form the windings for the driving coil and
the sensing coil. Solder is used to fuse the two sheets together to
complete the circuit for the windings. These are of course example
fluxgates and it will be realized by those versed in the nonlinear
sensor art that other fluxgates as well as different nonlinear
sensors may be employed according to the description herein.
As can be seen, fluxgates 18.sub.n are coupled through electronic
circuits 34.sub.n where the (voltage) readout of one fluxgate
signal 20.sub.n (i.e. the derivative signal of the flux detected by
the sensing coil of the fluxgate device) is amplified by
differential voltage amplifier 24.sub.n (such as an instrumentation
amplifier with a very high impedance). At this point, the amplifier
may be used to trim out any d.c. in the fluxgate output. Following
this, the signal is passed through an integrator 26.sub.n to
convert the derivative signal seen by the sensing coil back to a
"flux" form to conform this system closely to the model of equation
(1). The use of a "leaky" integrator at this stage helps to
minimize divergence caused by any small d.c. signal that might have
leaked through the voltage amplifier stage. Typically, the output
of the integrator is also accompanied by d.c. that is removed
before the signal is passed to the other fluxgates. This is
accomplished by employing a filter 28.sub.n such as a Sallen-Key
second-order high pass filter. This filter is placed immediately
after the integrator, with the filter parameters tuned to work at a
specific frequency (the mean oscillating frequency of the coupled
system). The signal then passes through amplifier 30.sub.n to
achieve adequate gain to drive the downstream adjacent fluxgate.
After this amplification stage, the signal passes through
voltage-to-current converter (V-I converter) 32.sub.n in its final
step to drive the primary (driving) coil of the next-in-line
fluxgate. This converter also has a gain factor but it is set at a
fixed value during the construction of the coupling circuits. The
gain is set at much less than unity so that one volt in the signal
does not convert to one ampere in the voltage-to-current converter
stage.
As can be seen, the setup repeats for the other two coupling
circuits for the remaining fluxgates and all values of the coupling
circuit parameters are closely matched from one set to the other.
Each stage of the coupling circuit also can be used with high speed
and high precision operational amplifiers to further minimize time
delay and to more closely conform the circuits to the model of
equation (1) as knowledge of state variable x.sub.i is known in the
model.
Referring now to FIGS. 3A-3C, a greater detailed embodiment of the
set-up of FIG. 3A is shown. Sensor system 36 of this figure
incorporates a summer 38 for summing a coupling circuit output (in
this example, the magnetic flux) corresponding to each of the n
nonlinear sensors of the system. In this figure, schematic-level
description is provided for V-I converters 32.sub.n, fluxgate
sensors 18.sub.n, instrumentation amplifiers 24.sub.n, integrators
26.sub.n, filters 28.sub.n, and amplifiers 30.sub.n. As can be seen
in this figure, a coupling circuit output 40 is tapped from each of
the coupling circuits and these are summed in summer 38 of this
figure. While the coupling circuit output is shown to be taken
after integrator 26.sub.n, system performance can also be assessed
by tapping the coupling circuit before the integrator.
The phenomena described herein can be extended to a wide class of
nonlinear dynamic sensor systems. For example, a system of coupled
overdamped Duffing sensing elements described via quartic
potentials: {dot over
(x)}.sub.1(t)=ax.sub.1-bx.sub.1.sup.3+.lamda.(x.sub.1-x.sub.2) {dot
over (x)}.sub.2(t)=ax.sub.2-bx.sub.2.sup.3+.lamda.(x.sub.2-x.sub.3)
{dot over
(x)}.sub.3(t)=ax.sub.3-bx.sub.3.sup.3+.lamda.(x.sub.3-x.sub.1)
(4)
The bifurcation mechanism leading to oscillations for this sensor
system is different from the fluxgate array described above;
nonetheless, the same qualitative features appear in the overall
response of the system. It has been observed that the oscillatory
behavior in the sensor system does not occur in a single unforced
sensor. Even when coupled, the number of elements, initial
conditions, and the type of coupling, all contribute to the
emergence of this behavior. Hence, the disclosure herein provides
new considerations in enhancing the utility and sensitivity of a
large class of nonlinear dynamic sensors, such as fluxgate
magnetometers for magnetic fields, ferroelectric detectors for
electric-fields, or piezo-electric detectors for acoustics
applications.
System resolution (defined as the mean residence times difference
in the stable states of a threshold detector into which the summed
output of the sensor system is fed) can be enhanced by carefully
tuning the array (via the system parameter .lamda.) to just beyond
the onset of the oscillations. This works particularly well, when
one has a reasonable a priori knowledge of the target signal values
involved in a particular application, or when the target signal can
be suitably gated (limited) to avoid saturating the system.
Referring to FIG. 3A, the coupling strength .lamda. may be adjusted
by altering the values of the resistors and capacitors used in the
coupling circuits 34. In the specific implementation described in
FIGS. 3A-3C by way of example, variable resistor 42 of amplifier
element 30 permits easy adjustment of .lamda..
As discussed, a variety of mechanisms is available to quantify a
target signal when using the sensor system described herein. The
target signal may be quantified via its effect on the frequency of
the induced system oscillations, as well as the shift in the mean
value of this frequency. The residence time readout method can also
be used to discern the target signal. As those skilled in the art
will realize, the circuitries required for these detection methods
are quite simple; in particular, no feedback circuit is
required.
Though in FIG. 1, sensing system 10 was described utilizing one-way
couplings 14 between nearest neighbor sensing elements 12, the
sensing system can employ a variety of other coupling/sensor
configurations. For example in FIGS. 6, a number of representative
configurations are presented. In FIG. 6A, there is shown
bidirectional coupling 44 between nearest-neighbor sensors. FIG. 6B
illustrates unidirectional (one-way) coupling for nearest neighbor
sensors combined with bidirectional (two-way) coupling between
non-nearest neighbor sensors. FIGS. 6C-E show unidirectional
(one-way) coupling between nearest neighbor sensors combined with
unidirectional (one-way) sensor coupling between every other
non-nearest neighbor. In all of the coupling/sensor configurations
described, the term "nearest neighbor" sensor takes on its
conventional meaning in the art.
Obviously, many modifications and variations of the invention are
possible in light of the above description. It is therefore to be
understood that within the scope of the appended claims, the
invention may be practiced otherwise than as has been specifically
described.
* * * * *